In the scoring of Donald Trump's summit in Singapore with Kim Jong Un, the commentariat has generally declared China to be the winner, even though president Xi Jinping was not even at the talks.

But this may be too simple a conclusion. The budding Trump-Kim rapprochement may yet give Beijing something to worry about.

The consensus view is that U.S. gave up a lot and got little in return. North Korea, gave up little and may have gained a lot, with the likely easing of sanctions and a relaxation in the U.S. military posture.

China, however, got just about everything it wanted, or so the pundits say -- a U.S. agreement to dial down tensions; a North Korea which will (for the moment) be less belligerent; and an agreement which effectively mirrored the plan for the peninsula it has been pushing for the last year.

Beijing's "freeze-for-freeze" proposal required Pyongyang to place its nuclear program in mothballs, while the U.S., with South Korea, pledged to put on hold its regular military exercises.

The brief Trump-Kim pact does exactly that, although any commitments that Pyongyang has made will have to be taken at their word for the moment, since there is no independent means yet to verify them.

Even better from the Chinese perspective, Kim continues to send signals that Pyongyang might finally be willing to open up its economy, something that Beijing has been urging on its neighbor for decades.

All that is true as far as it goes, but such analysis leaves out an important point. Beijing might have come out on top in Singapore, but going into the summit, it also had serious concerns about what might transpire there.

Those worries, although they have been alleviated in the short-term, remain.

Beijing's key concern has always been that any dialogue between the U.S. and North Korea might do more than just ease tensions on the peninsula. Just as Washington has always worried about Japan and China getting on too well, Beijing frets about North Korea getting too close to the U.S.

It is true, as so many have pointed out that, that Trump gave away a lot up front in his commit with Kim while getting little in return.

But such an approach could conceivably make sense if it is part of a longer term game, one in which Washington and North Korea leverage their relationship to keep China at bay.

The U.S. is already the security guarantor for South Korea. Why could it not play a similar role for the North? That is certainly an idea that would worry China.

Obviously, the two situations are not analogous. Washington helps protect the South against the North, not directly against China. Securing the North against Beijing would be a much bigger military challenge.

Most scenarios for a "grand bargain" on the peninsula, the kind of deal that is comprehensive but precludes reunification, contemplate a drawdown for the 25,000-odd U.S. troops still stationed in South Korea.

Trump himself has always made it clear that he would like to withdraw U.S. troops, perhaps even preceding any deal between all of the region's big players.

For Trump, the U.S. troops are an enduring symbol of his conviction that the U.S. gets a raw deal in Asia, in which Washington pays to protect its allies, while getting done over by them on trade at the same time.

This is music to China's ears. But for North Korea, the presence of the U.S. could be a useful counterbalance to Chinese dominance.

Beijing and Pyongyang used to boast in official propaganda that they were as close "as lips and teeth." It is not a phrase that you hear very often these days, for good reason.

Kim's madman antics over the last year, threatening nuclear war and the like, were never aimed just as the U.S. or South Korea and Japan. Students of the long-running drama on the Korean peninsula have long known that Pyongyang is just as happy to keep Beijing off balance.

Kim Il Sung, who established the Kim Dynasty in the north after the Pacific War and the end of Japanese colonial rule over the peninsula, always played the Soviet Union and China off against each other.

In the early 1990s, North Korea's xenophobic siege mentality, a feature of the regime since its birth, was accentuated by Beijing's decision to establish diplomatic ties with Seoul. China's willingness to push ahead with its own market reforms also grated on its determinedly Stalinist neighbor. The Kims never bought it.

Kim Jong Un might now be ready to embrace limited economic reform but he still worries about being overly dominated by the Chinese.

China retains huge economic leverage over North Korea, something Beijing demonstrated toward the end of last year, when they joined international sanctions and slowed the provision of essential commodities, like oil, in an effort to reign their errant neighbor in.

If Kim is to liberalize his economy, and even take tentative steps to wind down his nuclear arsenal, he will also need to diversify his friends. South Korea is important. Even Japan, a whipping boy for all Koreans, could be invited in.

Why not the Americans as well? If Kim wants to wean himself off China, then Washington might be his best friend of all. Now that's an idea that would scare president Xi. Perhaps he should have insisted on a seat at the table in Singapore after all.

Richard McGregor is a senior fellow for East Asia at the Lowy Institute in Sydney.